Model combination: Robert Mapplethorpe and Michelangelo

'Brilliantly composed and lit' ... Mapplethorpe's intimate portraits, including this one of Ken Moody (1983). Photograph: Robert Mapplethorpe Foundation

The naked bodies in the Accademia Gallery in Florence, home to Michelangelo's David, strain and contort and flex their muscles. Athletic flesh is posed in spectacular acts of prowess, the body constrained and tested in ways that have been part of the tradition of the nude since ancient times. But the flesh that shines in these images is not the work of Michelangelo. I am looking, in these proud surroundings, at photographs by Robert Mapplethorpe.

It's just been announced that Robert Mapplethorpe: Perfection in Form, the first ever exhibition of a modern artist in the gallery where – in addition to David – Michelangelo's unfinished Prisoners and Saint Matthew hold the stage, is to be extended by popular demand until January 2010. Apparently it has been a huge success since opening this May (although you wonder how they can tell: the Mapplethorpes are displayed in the same space as the Michelangelos, so you can't avoid buying entry with your museum ticket.)

There is plenty here to shock traditionalists. Good. When it comes to Michelangelo, the prudes and snobs have had their day. Here is an artist who needs to be reclaimed by the vulgar, or at least by the living. If nothing else, putting Mapplethorpe's pictures in this vicinity highlights the fierce carnality of Michelangelo's art, which has something to say to our own longings and anxieties when we look at naked bodies.

At last the Accademia has got its own back on the street vendors selling postcards and kitchen aprons with pictures of David's willy. Yeah, the museum seems to be saying, David is naked. And how. I think this is a great new direction for Florentine museums to take. It's much healthier than their habitual way of getting attention by restoring a work that doesn't visibly need restoration. Donatello's David in the Bargello has just been given this treatment, changing its appearance for ever. But when the Mapplethorpe show is over, the works of Michelangelo will be unchanged.

In a classic episode of The Simpsons, Marge leads a campaign to ban violence from the Itchy and Scratchy cartoons. But she is shocked when her erstwhile allies want to stop the statue Homer calls "Michelangelo's Dave" from coming to the Springfield Museum. Mapplethorpe's images were test cases of censorship in his lifetime: here they simply appear as brilliantly composed and lit photographs, ecstatically in love with beauty.

The only problem with the show is that it tries too hard to present the photographer as a "great" artist. In its reverence, it downplays the shock of his art. It is an impressive event – but it would be even better if Michelangelo's Prisoners were juxtaposed with Mapplethorpe's X Portfolio.